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I think you can take this one step further and talk about models that are actually false, but nonetheless work. Perhaps the best example would be calculus, whic
by lmkg 16y ago
I think you can take this one step further and talk about models that are actually false, but nonetheless work. Perhaps the best example would be calculus, which treats space as continuous, and in that sense is the polar opposite of the model of atoms. We now know that space is discretized (at the Plank-length scale, ~10^-36ish meters), but calculus nonetheless remains a remarkably effective and efficient model for making testable and verifiable predictions about mechanics (which itself is false but useful). So calculus is an example of the sort of "pedagogical device" that the 1860's philosophers were debating.
The takeaway from this is that models need not be based firmly in reality to be useful, and conversely that models that are useful and make correct predictions may still nonetheless be based on false descriptions. My favorite example of the latter is Lorentz transforms, which the author alluded to in the article. The math behind changing frames of reference in special relativity predates relativity itself, and were actually developed as a mathematical model of the now-defunct theory of "ether," the posited medium that light waves must move through and which happened to magically distort space with some sort of drag force. Despite the fact that its theoretical bases was completely false, Lorentz' (Lorentz's?) work nonetheless was an accurate model, and could be translated whole into a totally different theoretical framework.
Whether that new theoretical framework is accurate (i.e. "real") or not is hard to tell. It seems to be holding up to advanced scrutiny so far, but that's not a sure indicator.
- jules 16y ago> We now know that space is discretized We do not. That is merely the case in some controversial quantum gravity theories. However, I can give another example. In electrodynamics, you often treat a bulk charge as a continuous charge density (for example a charged sphere) rather than a large discrete set of point charges. This is because then you can apply calculus, which makes computations feasible.
- vilhelm_s 16y agoIt is said that Poincaré, when finally convinced that the evidence of atoms was overwhelming, exclaimed something like "but then it's all false!", meaning that all the continuum-based theories like fluid dynamics and electrodynamics, which had previously seemed like exact descriptions of the underlying reality, had suddenly shown themselves to be mere approximations...
- dkarl 16y agoThe takeaway from this is that models need not be based firmly in reality to be useful What, then, is the criterion for being "based in reality?" Isn't it safe to assume that the theories that say space is discretized are also false in some way? Also, a minor but important quibble: calculus itself is not a physical theory.
- deleted 16y ago[deleted]
- alphaBetaGamma 16y agoThe world is flat. False, but true enough when you are building a bridge.
- baddox 16y agoCalculus itself is rather geometrical. A definite integral is the area under a curve on a 2d graph of the real numbers, and the real numbers certainly are continuous. Obviously one can argue (and many do) about the relation between mathematics and the real world.